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2016
A model is set up which embodies the basic features of Adaptive quadrature routines involving mixed rules. Not before mixed quadrature rules basing on anti-Gaussian quadrature rule have been used for fixing termination criterionin Adaptive quadrature routines.
Singh, Bibhu Prasad, Dash, Rajani Ballav
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A model is set up which embodies the basic features of Adaptive quadrature routines involving mixed rules. Not before mixed quadrature rules basing on anti-Gaussian quadrature rule have been used for fixing termination criterionin Adaptive quadrature routines.
Singh, Bibhu Prasad, Dash, Rajani Ballav
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Blending product-type quadrature rules
BIT, 1982A product type (one dimensional) quadrature rule is one which approximates a finite integral of the integrand function f(x)g(x) by an inner \(f^ TWg\) when f and g are \(m\times 1\) and \(n\times 1\) matrices of function values respectively and W is a \(m\times n\) matrix of weight coefficients.
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1987
Recently Peherstorfer [1] derived a characterization of positive quadrature rules with knots in (a,b). An equivalent characterization will be presented using the positive definiteness of a matrix of moments. This is the one-dimensional case of a characterization of interpolatory cubature formulae, see, for example, [2] and [3].
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Recently Peherstorfer [1] derived a characterization of positive quadrature rules with knots in (a,b). An equivalent characterization will be presented using the positive definiteness of a matrix of moments. This is the one-dimensional case of a characterization of interpolatory cubature formulae, see, for example, [2] and [3].
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Error analysis of quadrature rules
International Journal of Mathematical Education in Science and Technology, 2004Approaches to the determination of the error in numerical quadrature rules are discussed and compared.
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Quadrature Rules with Multiple Nodes
2016In this paper a brief historical survey of the development of quadrature rules with multiple nodes and the maximal algebraic degree of exactness is given. The natural generalization of such rules are quadrature rules with multiple nodes and the maximal degree of exactness in some functional spaces that are different from the space of algebraic ...
Gradimir V. Milovanović +1 more
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Forming a mixed quadrature rule using an anti-gaussian quadrature rule
Bulletin of Pure & Applied Sciences- Mathematics and Statistics, 2017Bibhu Prasad Singh, Rajani Ballav Dash
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quadrature rules on unbounded intervals
2004After some remarks on the convergence order of the classical gaussian formula for the numerical evaluation of integrals on unbounded interval, the authors develop a new quadrature rule for the approximation of such integrals of interest in the practical applications.
M.R. Capobianco, G. Criscuolo
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On Generating Gaussian Quadrature Rules
1979Given a mass distribution dσ(x) on the (finite or infinite) interval (a,b), where σ(x) has at least n+1 points of increase, and assuming the existence of the first 2n moments of dσ(x), $${\mu _k} = \int_a^b {{x^k}} d\sigma (x),\;\;\;\;k = 0,1,2,...,2n - 1$$ (1.1) it is well known that the n-point Gaussian quadrature rule associated with the ...
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